Although Duhem recognized J. Clerk Maxwell’s ingenuity, he could not appreciate Maxwell’s theory at its real value because of its contradictions and unrigorous development, its mistakes in sign, and its lack of experimental foundation. Duhem preferred an electromagnetic theory due to Helmholtz, since it could be logically derived from the classical experiments. This theory, which Duhem helped to elaborate—and improve—is more general than Maxwell’s because it contains two additional arbitrary parameters. By an appropriate choice of values for these parameters, it can be shown that Maxwell’s equations appear as special cases of Helmholtz’ theory. In particular, if the Faraday-Mossotti hypothesis is adopted (equivalent to one parameter being infinity), then transverse fluxes propagate with the velocity of light. This results in an electromagnetic theory of light and an explanation of Heinrich Hertz’s experiments. If the other parameter (Helmholtz’) is chosen to be zero, then no longitudinal fluxes can be propagated, which circumstance is in agreement with Maxwell’s equations. Duhem, however, believed that there were experiments showing that such longitudinal fluxes exist and are also propagated at the velocity of light. He suggested (1902) that perhaps the recently discovered X rays might be identified with these longitudinal fluxes.

Duhem was a pitiless critic of Maxwell’s theory, claiming that it not only lacked rigorous foundation but was not sufficiently general to explain the existence of permanent magnets (Les théories électriques de J. Clerk Maxwell [1902]). Similar reservations about lack of rigor were expressed by many Continental physicists (e.g., Poincaré), and Helmholtz worked out his own electromagnetic theory because of his dissatisfaction with Maxwell’s approach. Duhem later admitted that not only had his criticisms not been accepted, they had not even been read or discussed; and of course Maxwell’s theory has triumphed. However, both L. Roy¹⁵ and A. O’Rahilly¹⁶ have contended that the logical derivation of Maxwell’s equations from a continuum viewpoint comes best through the Helmholtz-Duhem theory with the proper choice of constants.

15. L. Roy, L’électrodynamique des milieux isotropes en repos d’aprés Helmholtz et Duhem (Paris, 1923).

16. A. O’Rahilly, Electromagnetics (London, 1938), ch. 5; repr. as Electromagnetic Theory, 2 vols. (New York, 1965).

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